Stress reducing fastener assembly

ABSTRACT

A system includes a first structure having an upper surface coupled to a second structure by a fastener assembly including a bushing positioned within an opening in the upper surface of the first structure. An inner opening of the bushing defines an inner diameter, and a fastener is at least partially positioned within the bushing. An outer surface of the fastener defines an outer diameter of the fastener. The bushing and the fastener are configured such that a space between the outer surface of the fastener and the inner opening of the bushing defines a gap which increases in size in a direction extending from the upper surface to the lower surface of the first structure.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Contract No.W911W6-19-9-0005 awarded by the U.S. Army. The government has certainrights in the invention.

FIELD

The present disclosure relates generally to systems and methods ofcoupling a first structure to a second structure. More specifically, thepresent disclosure relates to a system and method of reducing localstress concentration experienced by a components in a fastener assemblyused to couple a first structure to a second structure.

BACKGROUND

Fasteners (e.g., lugs, bolts, screws, pins, etc.) may experience stressconcentrations when coupling a first structure to a second structure.Further, the first structure and the second structure may experiencestress concentrations proximate the fastener. For example, the loadexperienced by the fastener may cause the fastener to bend, therebycausing local stress concentration in the fastener, the first structure,and/or the second structure. This may result in decreased performance ofthe fastener, the first structure, and/or the second structure. Further,the local stress concentrations may cause damage to the first structureor the second structure that the fastener is coupled to.

SUMMARY

At least one embodiment relates to a system to fasten a first structureand a second structure, the system including a bushing positioned withinan opening in the upper surface of the first structure, wherein an inneropening of the bushing defines an inner diameter, and a fastener is atleast partially positioned within the bushing, wherein an outer surfaceof the fastener defines an outer diameter, wherein the bushing and thefastener are configured such that a space between the outer surface ofthe fastener and the inner opening of the bushing defines a gap, whereinthe gap increases in size in a direction extending from the uppersurface to the lower surface of the first structure.

According to various embodiments, the inner diameter of the bushingincreases in size in a direction extending from the upper surface to thelower surface of the first structure. According to various embodiments,the outer diameter of the fastener decreases in size in a directionextending from the upper surface the lower surface of the firststructure. According to various embodiments, the outer surface of thefastener and the inner opening of the bushing define a taper angle in adirection extending from the upper surface to the lower surface of thefirst structure, wherein the taper angle is between about zero degreesand about ten degrees. According to various embodiments, the taper angleis about 0.8 degrees. In some embodiments, the taper angle is betweenabout 0.1 and about 1 degrees, between about 0.1 and about 0.5 degrees,between about 0.5 and about 1 degrees, between about 1 and about 1.5degrees, or between about 1 and about 2 degrees. According to variousembodiments, the bushing is a first bushing and the fastener assemblyfurther includes a second bushing positioned within the opening in theupper surface of the first structure, and a retainer surrounding atleast a portion of the first bushing and the second bushing. Accordingto various embodiments, the first structure comprises compositematerial. According to various embodiments, the fastener comprisesmetallic material. According to various embodiments, the first structureis a rotor blade, and the fastener assembly is configured to couple thefirst structure to the second structure, the second structure being arotor head.

Another embodiment relates to a fastener assembly configured to couple arotor blade to a rotor head including a bushing positioned within anopening in the rotor blade, wherein an inner opening of the bushingdefines an inner diameter, and a fastener is at least partiallypositioned within the bushing and at least partially positioned withinthe rotor head, wherein an outer surface of the fastener defines anouter diameter, wherein the bushing and the fastener are configured suchthat a space between the outer surface of the fastener and the inneropening of the bushing defines a gap, wherein the gap increases in sizein a direction away from an upper surface of the rotor blade.

According to various embodiments, the inner diameter of the bushingincreases in size in a direction away from the upper surface of thefirst structure. According to various embodiments, the outer diameter ofthe fastener decreases in size in a direction away from the uppersurface. According to various embodiments, the outer surface of thefastener and the inner opening of the bushing define a taper angle thatis about 0.8 degrees.

Another embodiment relates a method of coupling a first structure to asecond structure, including providing a bushing within an opening in anupper surface of the first structure, wherein an inner opening of thebushing defines an inner diameter, and providing a fastener at leastpartially within the bushing, wherein an outer surface of the fastenerdefines an outer diameter, wherein the bushing and the fastener areconfigured such that a space between the outer surface of the fastenerand the inner opening of the bushing defines a gap, wherein the gapincreases in size in a direction away from the upper surface of thefirst structure.

According to various embodiments, the inner diameter of the bushingincreases in size in a direction away from the upper surface of thefirst structure. According to various embodiments, the outer diameter ofthe fastener decreases in size in a direction away from the uppersurface. According to various embodiments, the outer surface of thefastener and the inner opening of the bushing define a taper angle,wherein the taper angle is approximately 0.8 degrees. According tovarious embodiments, the bushing is a first bushing and the methodfurther includes providing a second bushing within the opening in theupper surface of the first structure, and providing a retainersurrounding a portion of the first bushing and the second bushing.According to various embodiments, the first structure comprisescomposite material. According to various embodiments, the fastenercomprises composite material.

This summary is illustrative only and should not be regarded aslimiting.

BRIEF DESCRIPTION OF THE FIGURES

The disclosure will become more fully understood from the followingdetailed description, taken in conjunction with the accompanyingfigures, wherein like reference numerals refer to like elements, inwhich:

FIG. 1 is a cross sectional view of a fastener assembly, according to anexample embodiment.

FIG. 2 is an exploded view of the fastener assembly of FIG. 1, accordingto an example embodiment.

FIG. 3A is a cross sectional view of the fastener assembly of FIG. 1 inan unloaded state, according to an example embodiment.

FIG. 3B is a partial cross sectional view of the fastener assembly ofFIG. 1 in an unloaded state, according to an example embodiment.

FIG. 4 is a cross sectional view of the fastener assembly of FIG. 1 in aloaded state with exaggerated deformation, according to an exampleembodiment.

FIG. 5 is a pressure distribution depiction of a structure showingpressure concentrations over a portion thereof.

FIG. 6 is a pressure distribution depiction of a structure showingpressure concentrations over a portion thereof.

FIG. 7 is a pressure distribution depiction of the structure of FIG. 6showing pressure concentrations over a portion thereof.

FIG. 8 is a perspective view of a rotor assembly, according to anexample embodiment.

FIG. 9 is a perspective view of a fastener assembly, according to anexample embodiment.

FIG. 10 is a cross sectional view of an arm coupled to a blade spar,according to an example embodiment.

DETAILED DESCRIPTION

Before turning to the figures, which illustrate certain exemplaryembodiments in detail, it should be understood that the presentdisclosure is not limited to the details or methodology set forth in thedescription or illustrated in the figures. It should also be understoodthat the terminology used herein is for the purpose of description onlyand should not be regarded as limiting.

Fastener assemblies include fasteners (e.g., lugs, bolts, screws, pins,etc.) that can be used to couple a first structure to a secondstructure. According to various embodiments, the fasteners, the firststructure, the second structure, and other components of the fastenerassembly, may experience loads while coupling the structures as a resultof forces acting on the first structure, the second structure, and/orthe fastener. For example, a fastener may be used to couple a rotor headto a blade (e.g., as a part of a helicopter, wind turbine, fixed wingaircraft propellers, etc.). In this example, the fastener may be in aloaded state as a result of various forces (e.g., the weight of thespar, the weight of the blade, centripetal force resulting from rotationof the blade, etc.). The loads experienced by fastener may cause thefastener to deflect (e.g., bend), which may result in undesired localstress concentrations in the fastener. Further, the bending of thefastener may result in local stress concentrations in the firststructure and the second structure, which may be particularlyundesirable if the first structure and/or the second structure ismanufactured from a composite material. According to variousembodiments, a fastener may be positioned within an inner opening of abushing, which may be positioned within an opening of a structure.

In a loaded state, the fastener may bend such that only a relativelysmall portion of the outer surface of the fastener contacts the inneropening of the bushing, compared to the when the fastener assembly in anunloaded state. In this example, the fastener may have a localizedstress concentration proximate the portion of the fastener that iscontacting the bushing under the loaded condition, which may result indegraded performance of the fastener assembly. Further, the firststructure and the second structure may experience localized stressconcentration(s) proximate one or more portions of the fastenercontacting the bushing under the loaded condition, which may result indegraded performance of the first structure and/or the second structure.Thus, according to various embodiments described herein, a fastenerassembly that reduces localized stress concentrations is disclosed.

According to various embodiments, fastener assemblies may includevarious components manufactured from composite materials (e.g., carbonfiber, poly-paraphenylene terephthalamide (K29) (e.g. Kevlar®),fiberglass, etc.). Advantageously, composite structures may have arelatively high strength to weight ratio when compared to othermaterials (e.g., metal). However, composite structures may be weak incertain directions and susceptible to partial or complete failure undercertain directional loads. For example, composite materials, especiallylarge structures manufactured from composite materials, may be moresusceptible to shear (e.g., interlaminar shear) or fracture under heavyloads than metal components, especially if the composite structureexperiences local stress concentrations. Thus, when a fastener assemblyincludes composite components, reducing local stress concentrations mayreduce the risk of shear or fracture.

Referring generally to the figures, systems and methods of reducing thestress concentration experienced by the components in a fastenerassembly, including a first structure, a second structure, and afastener used to couple the first structure to the second structure aredisclosed herein. According to various embodiments, the fastenerassembly includes a fastener that is received within an inner opening ofa bushing. According to various embodiments, the inner opening of thebushing is tapered such that a gap exists between the fastener and thebushing when the fastener assembly in an unloaded state. The inneropening of the bushing may be tapered to have a taper angle, which canbe tailored based on expected loads that the fastener may experience. Inthis example, the size of the gap between the fastener and the bushingmay not be constant throughout the fastener assembly. For example, thesize of the gap may be smallest near the top of the fastener assemblyand the gap may increase in size up until a specific depth. By tailoringthe draft angle based on expected loads, when the fastener bends in aloaded state, a larger portion of the fastener contacts the bushing thanif there was no draft angle, thereby by reducing the localized stressconcentration of the first structure, the second structure, and thefastener. According to various embodiments, the fastener may be taperedinstead of, or in addition to, the bushing being tapered to furtherreduce local stress concentrations in the fastener assembly.

Referring now to FIGS. 1 and 2, a cross sectional view and an explodedview, respectively, of a fastener assembly 100 are shown, according toan example embodiment. The fastener assembly 100 may be used to couple afirst structure 106 to a second structure 108. According to variousembodiments, the first structure 106 and the second structure 108 are apart of a blade assembly (e.g., as a part of a helicopter, wind turbine,fixed wing aircraft propellers, etc.). For example, the first structure106 may be a part of the blade (e.g., the blade spar 700 shown in FIG.10) and the second structure 108 may be a part of the rotor head (e.g.,the arm 502 shown in FIG. 8). In this example embodiment, the fastenerassembly 100 is used to couple the rotor head to the blade such thatenergy may be transferred between the rotor head and the blade throughthe fastener assembly 100.

The fastener assembly 100 includes a fastener 102 (e.g., lug, bolt,screw, pin, etc.) used to couple the first structure 106 to the secondstructure 108. As shown in FIG. 1, when assembled, a first portion 126(see FIG. 2) of the fastener 102 is positioned within an opening 160(see FIG. 2) in the first structure 106 and a second portion 128 (seeFIG. 2) of the fastener 102 is positioned within the second structure108. As shown, the opening 160 is generally elliptical, however, inother embodiments, the opening 160 may be circular or have anothershape. As will be discussed further herein, the fastener 102 may besubjected to various forces while coupling the first structure 106 tothe second structure 108.

For example, when the fastener assembly 100 is used in a blade assembly,rotation of the blades, including the first structure 106 and the secondstructure 108, may result in a load being applied to the fastener 102 asa result of the centripetal forces resulting from the rotation of theblades, as will be discussed further below with respect to FIG. 4. Thefastener 102 includes a flange 124 (see FIG. 2). The bottom surface ofthe flange 124 is flush with an upper surface 107 of the first structure106 when installed into the first structure 106. The outer surface ofthe fastener 102 defines an outer diameter 120 of the fastener 102. Itshould be appreciated that the outer diameter 120 may be constantthroughout the fastener 102 or the outer diameter 120 may vary thoughought the fastener 102. For example, as shown in FIG. 2, the outerdiameter 120 is larger in the first portion 126 of the fastener 102 thanthe second portion 128 of the fastener 102. As shown, the fastener 102includes an inner opening 121 such that the fastener 102 is at leastpartially hollow, such that an inner opening 121 of the fastener 102defines an inner diameter 122.

According to various embodiments, a hollow fastener 102 may beadvantageous due to the fastener 102 being relatively light compared toa solid fastener. According to various embodiments, the fastener may berelatively large. For example, the outer diameter 120 of the fastener102 may be between about one and about six inches. According to anexample embodiment, the outer diameter 120 of the fastener 102 is about1.5 inches. According to various embodiments, the fastener 102 may bepartially or completely manufactured from metal (e.g., aluminum, steel,titanium, etc.). In various embodiments, the fastener 102 may bepartially or completely manufactured from composite material (e.g.,carbon fiber, poly-paraphenylene terephthalamide (K29) (e.g. Kevlar®made by DuPont de Nemours, Inc. of Wilmington, Del.), fiberglass, etc.).

The fastener assembly 100 further includes a first bushing 104 (e.g., aninner bushing) that is configured to receive a portion of the fastener102. For example, as shown in FIG. 1, the first bushing 104 may bereceived by the opening 160 in the first structure 106 such that aportion of the first bushing 104 is positioned between the firststructure 106 and the fastener 102. As shown, the first bushing 104 is aflanged bushing, which includes a flange 144, however, according tovarious embodiments, other types of bushings may be used. As shown, whenthe first bushing 104 is installed into the first structure 106, thebottom surface of the flange 144 is flush with the upper surface 107 ofthe first structure 106, thereby preventing the first bushing 104 fromsliding into the first structure 106.

As is discussed further below, the first bushing 104 may facilitatedistributing the force of the fastener 102 on the first structure 106 tomitigate local stress concentrations in both the fastener 102 and thefirst structure 106. As shown in FIG. 1, the outer surface of the firstbushing 104 defines an outer diameter 140. According to variousembodiments, the outer diameter 140 may remain constant through some orall of the first bushing 104. As shown, the first bushing 104 has aninner opening 146 (see FIG. 2) that defines an inner diameter 142.According to various embodiments, the inner diameter 142 variesthroughout the first bushing 104. For example, as shown and discussedfurther below with respect to FIG. 3, the inner diameter 142 is smallestproximate the flange 144 and increases in size in a direction away fromthe flange 144. According to various embodiments, the first bushing 104may be partially or completely manufactured from metal (e.g., aluminum,steel, titanium, etc.). In various embodiments, the first bushing 104may be partially or completely manufactured from composite material(e.g., carbon fiber, poly-paraphenylene terephthalamide (K29) (e.g.Kevlar®), fiberglass, etc.).

The fastener assembly 100 further includes a second bushing 110 (e.g.,an outer bushing) that is configured to receive a portion of the firstbushing 104. For example, the second bushing 110 includes an opening 141(see FIG. 2) that is configured to receive the outer surface of thefirst bushing 104. As shown, a portion of the first bushing 104 ispositioned within a portion of the second bushing 110. As shown, thesecond bushing 110 includes a flange 154. As shown, when the secondbushing 110 is installed into the first structure 106, the upper surfaceof the flange 154 is flush with a lower surface 109 of the firststructure 106, thereby preventing the second bushing 110 from slidinginto the first structure 106. According to various embodiments, thesecond bushing 110 may be partially or completely manufactured frommetal (e.g., aluminum, steel, titanium, etc.). In various embodiments,the second bushing 110 may be partially or completely manufactured fromcomposite material (e.g., carbon fiber, poly-paraphenyleneterephthalamide (K29) (e.g. Kevlar®), fiberglass, etc.).

The fastener assembly 100 further includes a retention ring (e.g., abushing, a retainer, etc.) 112 that is configured to receive a portionof the first bushing 104 and a portion of the second bushing 110. Asshown, the retention ring 112 includes an inner opening 113 (see FIG. 2)configured to surround the outer surface of the second bushing 110, suchthat a portion of the first bushing 104 and the second bushing 110 aresimultaneously positioned within the retention ring 112 when thefastener assembly 100 is installed. The retention ring 112 is sized tofit within an opening of the first structure 106. For example, theretention ring 112 may be pressure fit into the opening of the firststructure 106, thereby securing the first bushing 104 and the secondbushing 110 within the opening in the first structure.

As shown, the outer diameter of the retention ring 112 is generallyelliptical such that the retention ring 112 fits within the ellipticalopening 160, however, in other embodiments, the retention ring 112 maybe circular. Further, the inner opening 113 is generally circular.According to various embodiments, the retention ring 112 may bepartially or completely manufactured from metal (e.g., aluminum, steel,titanium, etc.). In various embodiments, the retention ring 112 may bepartially or completely manufactured from composite material (e.g.,carbon fiber, poly-paraphenylene terephthalamide (K29) (e.g. Kevlar®),fiberglass, etc.). It should be appreciated that the retention ring 112may be omitted according to various embodiments.

The fastener assembly 100 further includes a third bushing 114positioned within an opening of the second structure 108 and configuredto receive a portion of the fastener 102. As shown, the third bushing114 includes a flange 164. As shown, when the third bushing 114 isinstalled into the second structure 108, the lower surface of the flange164 is flush with the upper surface of the second structure 108, therebypreventing the third bushing 114 from sliding into the second structure108. According to various embodiments, the third bushing 114 may bepartially or completely manufactured from metal (e.g., aluminum, steel,titanium, etc.). In various embodiments, the third bushing 114 may bepartially or completely manufactured from composite material (e.g.,carbon fiber, poly-paraphenylene terephthalamide (K29) (e.g. Kevlar®),fiberglass, etc.).

Referring now to FIGS. 3A and 3B, a cross sectional view and a partialcross sectional view, respectively, of the fastener assembly 100 isshown in an unloaded state, according to an example embodiment. Theunloaded state is a state in which the fastener 102 experiencesrelatively low forces as compared to the loaded state. For example, in ablade assembly (e.g., as a part of a helicopter, wind turbine, fixedwing aircraft propellers, etc.), the unloaded state may be when theblades are motionless and the loaded state may be when the blades arespinning. As shown, in the unloaded state, there is a gap 200 betweenthe fastener 102 and the first bushing 104. As shown, the gap 200 is aresult of the inner diameter 142 of the first bushing 104 increasing ina direction away from the upper surface 107 of the first structure 106while the outer diameter 120 of the portion of the fastener 102positioned within the first bushing 104 remains constant.

However, it should be appreciated that a similar gap 200 may be achievedby providing a fastener 102 with an outer diameter 120 that decreases insize away from the upper surface 107 of the first structure 106. Asshown, the gap 200 increases in a direction away from the upper surface107 of the first structure 106, such that the outer diameter 120 of thefastener 102 and the inner diameter 142 of the first bushing 104 definesa taper angle 202 (see FIG. 3B). As is discussed below, the taper angle202 may be tailored based on expected conditions in the loaded state tominimize local stress concentrations in the fastener 102 and the firststructure 106. For example, the taper angle 202 may be between aboutzero and about twenty degrees. For example, the taper angle 202 may bebetween zero and ten degrees. For example, the taper angle may bebetween zero and three degrees. According to at least one embodiment,the taper angle 202 is about 0.8 degrees. According to variousembodiments, the taper angle 202 is 0.1 degrees, 0.2 degrees, 0.3degrees, 0.4 degrees, 0.5 degrees, 0.6 degrees, 0.7 degrees, 0.9degrees, 1 degrees, 1.1 degrees, 1.2 degrees 1.3 degrees, 1.4 degrees,1.5 degrees, 1.6 degrees, 1.7 degrees, 1.8 degrees, 1.9 degrees, or 2degrees. According to various embodiments, the magnitude of the taperangle 202 may be tailored based on anticipated bend of the fastener 102.

Referring now to FIG. 4, a cross sectional view of the fastener assembly100 is shown in a loaded state, according to an example embodiment. Asshown, in the loaded state, a first force F1 is acting on the firststructure 106 and a second force F2 is acting on the second structure108. For example, in a blade assembly, the first force F1 may be atleast partially attributable to the centrifugal force acting upon thefirst structure 106 (e.g., a blade) and the second force F2 may be equaland opposite of the first force F1. As shown, in the loaded state, thefirst force F1 and the second force F2 may cause the fastener 102 tobend. In this example embodiment, the fastener 102 bends such that thegap 200 increases in size on a first side of the fastener 102 (e.g., theleft side of the fastener 102 as shown in FIG. 4) and decreases in sizeon the opposite side (e.g., the second side) of the fastener 102 (e.g.,the right side of the fastener 102 as shown in FIG. 4). Further, underin the loaded state, the fastener 102 becomes angled within the firstbushing 104.

Due to the taper angle 202 (see FIG. 3), the contact area between thefastener 102 and the first bushing 104 is larger than if there was notaper angle 202. For example, if there were no taper angle 202, only arelatively small portion of the bottom of the first bushing 104 wouldcontact the fastener 102. However, the taper angle 202 (see FIG. 3),results in a larger portion of the first bushing 104 being in contactwith the fastener 102, thereby resulting in a more uniform pressuredistribution on the fastener 102 and the first bushing 104, whichdecreases local stress concentrations in the fastener 102, the firstbushing 104, the second bushing 110, the retention ring 112, and thefirst structure 106.

According to various embodiments, the taper angle 202 (see FIG. 200) istailored based on expected loads that the fastener 102 may experience inthe loaded condition. For example, in a blade assembly, the taper angle202 may be tailored based on maximum expected rotor, which would resultin a maximum first force F1 and a maximum second force F2 acting on thefastener 102. According to various embodiments, tailoring the taperangle 202 may include modeling the fastener assembly 100 and performingfinite element analysis under loaded conditions.

Referring now to FIGS. 5-7, representative pressure distributiondepictions of a structure (e.g., the first structure 106) are shown.Each pressure distribution depiction shows the relative pressure zonesexperienced by the structure under different conditions. In particular,the structure shown in FIG. 5 is a structure 400 that is coupled toanother structure via a fastener (e.g., the fastener 102) providedwithin a non-tapered bushing as discussed below. The structure shown inFIGS. 6-7 is a structure 300 that is coupled to another structure via afastener provided within a tapered bushing as discussed below. Thestructures 300, 400 may be coupled to another structure (e.g., thesecond structure 108) via a fastener (e.g., the fastener 102) as a partof a fastener assembly (e.g., the fastener assembly 100).

The pressure distribution depictions in FIGS. 5-7 show the relativepressure zones (e.g., shown as a pressure gradient) experienced by thestructures 300, 400 in the loaded state. As shown, the pressuredistribution depiction of the structures 300, 400 includes a maximumpressure zone 302, 402 (e.g., the surface area of the structures 300,400 that experiences the highest pressure), an intermediate pressurezone 304, 404 (e.g., the surface area of the structures 300, 400 thatexperiences relatively average pressure), and a minimum pressure zone306 (e.g., the surface area of the structures 300, 400 that experiencesthe least pressure).

Referring now to FIG. 5, a pressure distribution depiction of thestructure 400 under loaded conditions is shown. In the depiction in FIG.5, the structure 400 may be coupled to another structure via a fastener.The fastener may be positioned within a bushing that has a uniform innerdiameter (i.e., a non-tapered bushing). As shown the structure 400 mayexperience relatively high local stress concentrations compared to whenthe structure is coupled to another structure via a fastener locatedwithin a tapered bushing (e.g., the structure 300 shown in FIGS. 6 and7, discussed below). As shown, the maximum pressure zone 402 isrelatively concentrated over a relatively small surface area, therebyresulting in local stress concentration. Further, as shown, the minimumpressure zone 406 may experience no pressure, according to variousembodiments. The local stress concentrations may be a result of thebending of the fastener within the structure 400 under the loadedcondition, which results in reduced surface area contact between thefastener 400 and the bushing.

Referring now to FIG. 6, a pressure distribution depiction of thestructure 300 under loaded conditions is shown, according to an exampleembodiment. In the embodiment shown in FIG. 6, the structure 300 may becoupled to another structure via a fastener. The fastener may bepositioned within a tapered bushing (e.g., the first bushing 104). Forexample, the bushing may have a taper angle (e.g., the taper angle 202)of 0.4 degrees. As shown the structure 300 may experience relativelylower local stress concentrations compared to a when the structure iscoupled to another structure via a fastener located within a non-taperedbushing (e.g., the fastener 400 shown in FIG. 5, discussed above). Asshown, the maximum pressure zone 302 is distributed over a largersurface area than in FIG. 5, thereby resulting in reduced local stressconcentrations. It should be appreciated that the maximum pressure zone302 in FIG. 6 may experience a lower pressure than the maximum pressurezone 302 in FIG. 5. Further, as shown, the average pressure zone 304 isdistributed over a larger surface area of the structure than in FIG. 5.

Referring now to FIG. 7, a pressure distribution depiction of thestructure 300 under loaded conditions is shown, according to an exampleembodiment. In the embodiment shown in FIG. 7, the structure 300 may bycoupled to another structure via a fastener. The fastener may bepositioned within a tapered bushing (e.g., the first bushing 104). Forexample, the bushing may have a taper angle (e.g., the taper angle 202)of 0.8 degrees. As shown the structure 300 may experience relativelylower local stress concentrations compared to a structure 300 that iscoupled to another structure via a fastener located within a taperedbushing having a smaller taper angle (e.g., the fastener 300 shown inFIG. 6, discussed above). As shown, the maximum pressure zone 302 isdistributed over a larger surface area than in FIG. 6, thereby resultingin local stress concentration. It should be appreciated that the maximumpressure zone 302 in FIG. 7 may experience a lower pressure than themaximum pressure zone 302 in FIG. 6. Further, as shown, the averagepressure zone 304 is distributed over a larger surface area of thefastener than in FIG. 5.

Referring now to FIG. 8, a perspective view of a rotor assembly 500 isshown, according to an example embodiment. The rotor assembly 500 may bea part of a helicopter propulsion system (not shown). As shown, therotor assembly 500 includes a first mast 504 and a second mast 506 thatare configured to rotate. According to various embodiments, the firstmast 504 and the second mast 506 may rotate in the same direction or inopposite directions (e.g., the first mast 504 spins clockwise and thesecond mast 506 spins counter clockwise). As shown, a plurality of arms502 (e.g., hub arm assemblies) are coupled to the first mast 504 and thesecond mast 506 such that the plurality arms 502 spin as the first mast504 and the second mast 506 spin. As shown, each arm 502 is coupled to astructure 508. The structure 508 may be the same or similar to thesecond structure 108 described above. The structure 508 defines anaperture 510. For example, the aperture 510 may be defined by a centralopening in a structure 508. The aperture 510 may be configured toreceive one or more components of a fastener assembly (e.g., thefastener assembly 100) such that the arm 504 may be coupled to anotherstructure (e.g., the first structure 106 or the blade spar 700 shown inFIG. 10).

Referring now to FIG. 9, a perspective view of a fastener assembly 520is shown coupled to the arm 502 according to an example embodiment. Asshown, the structure 508 is coupled to the fastener assembly 520. Thefastener assembly 520 may be the same or similar to the fastenerassembly 100 described above. The fastener assembly 520 includes afastener 522. The fastener 522 is received by the aperture 510 in thestructure 508. The fastener 522 may couple the arm 502 and the structure508 to another structure (e.g., the first structure 106 or the bladespar 700 shown in FIG. 10). The fastener 522 may be the same or similarto the fastener 102 described above. The fastener 522 may be positionedwithin a first bushing 524. The first bushing 524 may be the same orsimilar to the first bushing 104 discussed above. For example, the firstbushing 524 may have a taper angle (e.g., the taper angle 202) thatresults in a gap (e.g., the gap 200) between the fastener 522 and thefirst bushing 524.

Referring now to FIG. 10, a cross sectional view of an arm 504 coupledto a blade spar 700 is shown, according to an example embodiment. Theblade spar 700 may be a part of a helicopter blade assembly. Accordingto various embodiments, the blade spar 700 is manufactured from acomposite material (e.g., carbon fiber, poly-paraphenyleneterephthalamide (K29) (e.g. Kevlar® made by DuPont de Nemours, Inc. ofWilmington, Del.), fiberglass, etc.). As shown, the blade spar 700 iscoupled to the structure 508 via the fastener assembly 520. As shown,the fastener assembly includes the first bushing 524. As discussedabove, the first bushing 524 may include a taper angle, which may reducelocal stress concentrations in the blade spar 700 similar as isdescribed above with respect to FIGS. 1-7. The fastener assembly 520further includes a second bushing 530 and a third bushing 534, which maybe the same or similar to the second bushing 110 and the third bushing114 described above.

Various numerical values herein are provided for reference purposesonly. Unless otherwise indicated, all numbers expressing quantities ofproperties, parameters, conditions, and so forth, used in thespecification and claims are to be understood as being modified in allinstances by the term “about” or “approximately.” Accordingly, unlessindicated to the contrary, the numerical parameters set forth in thefollowing specification and attached claims are approximations. Anynumerical parameter should at least be construed in light of the numberreported significant digits and by applying ordinary roundingtechniques. The term “about” or “approximately” when used before anumerical designation, e.g., a quantity and/or an amount includingrange, indicates approximations which may vary by (+) or (−) 10%, 5%, or1%.

As will be understood by one of skill in the art, for any and allpurposes, particularly in terms of providing a written description, allranges disclosed herein also encompass any and all possible subrangesand combinations of subranges thereof. Any listed range can be easilyrecognized as sufficiently describing and enabling the same range beingbroken down into at least equal halves, thirds, quarters, fifths,tenths, etc. As a non-limiting example, each range discussed herein canbe readily broken down into a lower third, middle third and upper third,etc. As will also be understood by one skilled in the art all languagesuch as “up to,” “at least,” “greater than,” “less than,” and the likeinclude the number recited and refer to ranges which can be subsequentlybroken down into subranges as discussed above. Finally, as will beunderstood by one skilled in the art, a range includes each individualmember.

As utilized herein with respect to structural features (e.g., todescribe shape, size, orientation, direction, relative position, etc.),the terms “approximately,” “about,” “substantially,” and similar termsare meant to cover minor variations in structure that may result from,for example, the manufacturing or assembly process and are intended tohave a broad meaning in harmony with the common and accepted usage bythose of ordinary skill in the art to which the subject matter of thisdisclosure pertains. Accordingly, these terms should be interpreted asindicating that insubstantial or inconsequential modifications oralterations of the subject matter described and claimed are consideredto be within the scope of the disclosure as recited in the appendedclaims.

It should be noted that the term “exemplary” and variations thereof, asused herein to describe various embodiments, are intended to indicatethat such embodiments are possible examples, representations, orillustrations of possible embodiments (and such terms are not intendedto connote that such embodiments are necessarily extraordinary orsuperlative examples).

The term “coupled” and variations thereof, as used herein, means thejoining of two members directly or indirectly to one another. Suchjoining may be stationary (e.g., permanent or fixed) or moveable (e.g.,removable or releasable). Such joining may be achieved with the twomembers coupled directly to each other, with the two members coupled toeach other using a separate intervening member and any additionalintermediate members coupled with one another, or with the two memberscoupled to each other using an intervening member that is integrallyformed as a single unitary body with one of the two members. If“coupled” or variations thereof are modified by an additional term(e.g., directly coupled), the generic definition of “coupled” providedabove is modified by the plain language meaning of the additional term(e.g., “directly coupled” means the joining of two members without anyseparate intervening member), resulting in a narrower definition thanthe generic definition of “coupled” provided above.

References herein to the positions of elements (e.g., “top,” “bottom,”“above,” “below”) are merely used to describe the orientation of variouselements in the FIGURES. It should be noted that the orientation ofvarious elements may differ according to other exemplary embodiments,and that such variations are intended to be encompassed by the presentdisclosure.

Although the figures and description may illustrate a specific order ofmethod steps, the order of such steps may differ from what is depictedand described, unless specified differently above. Also, two or moresteps may be performed concurrently or with partial concurrence, unlessspecified differently above.

It is important to note that any element disclosed in one embodiment maybe incorporated or utilized with any other embodiment disclosed herein.Although only one example of an element from one embodiment that can beincorporated or utilized in another embodiment has been described above,it should be appreciated that other elements of the various embodimentsmay be incorporated or utilized with any of the other embodimentsdisclosed herein. Other modifications are contemplated without departingfrom the scope and spirit of the present disclosure.

What is claimed is:
 1. A system to fasten a first structure and a secondstructure, the system comprising: a bushing positioned within an openingin an upper surface of the first structure, an inner opening of thebushing defining an inner diameter; and a fastener at least partiallypositioned within the bushing, an outer surface of the fastener definingan outer diameter of the fastener, the bushing and the fastener beingconfigured such that a space between the outer surface of the fastenerand the inner opening of the bushing defines a gap, the gap beingdimensioned to increase in size in a direction extending from the uppersurface to a lower surface of the first structure.
 2. The system ofclaim 1, wherein the inner diameter of the bushing increases in size inthe direction extending from the upper surface to the lower surface ofthe first structure.
 3. The system of claim 1, wherein the outerdiameter of the fastener decreases in size in the direction extendingfrom the upper surface to the lower surface of the first structure. 4.The system of claim 1, wherein the outer surface of the fastener and theinner opening of the bushing define a taper angle in the directionextending from the upper surface to the lower surface of the firststructure, wherein the taper angle is between about zero degrees andabout ten degrees.
 5. The system of claim 4, wherein the taper angle isabout 0.8 degrees.
 6. The system of claim 1, wherein the bushing is afirst bushing and the system further comprises: a second bushingpositioned within the opening in the upper surface of the firststructure; and a retainer surrounding at least a portion of the firstbushing and the second bushing.
 7. The system of claim 1, wherein thefirst structure comprises composite material.
 8. The system of claim 1,wherein the fastener comprises metal material.
 9. The system of claim 8,wherein the first structure is a rotor blade, and the second structureis a rotor head.
 10. A fastener assembly configured to couple a rotorblade to a rotor head comprising: a bushing positioned within an openingin the rotor blade, an inner opening of the bushing defines an innerdiameter; and a fastener at least partially positioned within thebushing and at least partially positioned within the rotor head, anouter surface of the fastener defining an outer diameter, the bushingand the fastener being configured such that a space between the outersurface of the fastener and the inner opening of the bushing defines agap, wherein the gap changes in size in a direction away from an uppersurface of the rotor blade.
 11. The fastener assembly of claim 10,wherein the inner diameter of the bushing increases in size in thedirection away from the upper surface of the rotor blade.
 12. Thefastener assembly of claim 10, wherein the outer diameter of thefastener decreases in size in the direction away from the upper surface.13. The fastener assembly of claim 11, wherein the outer surface of thefastener and the inner opening of the bushing define a taper angle thatis about 0.8 degrees.
 14. A method of coupling a first structure to asecond structure, comprising: providing a bushing within an opening inan upper surface of the first structure, an inner opening of the bushingdefining an inner diameter; and providing a fastener at least partiallywithin the bushing, an outer surface of the fastener defining an outerdiameter, the bushing and the fastener being configured such that aspace between the outer surface of the fastener and the inner opening ofthe bushing defines a gap dimensioned to increase in size in a directionaway from the upper surface of the first structure.
 15. The method ofclaim 14, wherein the inner diameter of the bushing increases in size inthe direction away from the upper surface of the first structure. 16.The method of claim 14, wherein the outer diameter of the fastenerdecreases in size in the direction away from the upper surface.
 17. Themethod of claim 14, wherein the outer surface of the fastener and theinner opening of the bushing define a taper angle, wherein the taperangle is approximately 0.8 degrees.
 18. The method of claim 14, whereinthe bushing is a first bushing and the method further comprises:providing a second bushing within the opening in the upper surface ofthe first structure; and providing a retainer surrounding a portion ofthe first bushing and the second bushing.
 19. The method of claim 14,wherein the first structure comprises composite material.
 20. The methodof claim 14, wherein the fastener comprises metal material.